Since this is a definition question, I’m going to put in a disclaimer that definitions in our community are rarely set in stone and often highly-debated, and these definitions in particular tie into classical literature which is pretty much the most debatable thing in the history of anything (look at how many times Homer has been translated into English!) so please take my answer as a generalization, not an ultimatum.“Sapphic” is an adjective for women/femmes that basically means “women-loving”. It’s broadly analogous to the terms “gynosexual” and “gynoromantic”, though unlike those (much newer) terms it doesn’t distinguish between sexual and romantic attraction.

“Sapphic love” basically means “love between women/femmes”. I, a bisexual woman who loves women, am sapphic, and lesbian women would be as well.

The term derives from Sappho, a poetess from the Archaic Period who wrote a lot of homoerotic poetry (of which we have sadly recovered very little). She lived on the island of Lesbos, hence the term “lesbian”, though the question of whether Sappho herself was exclusively attracted to women is kind of a can of worms not worth getting into on this blog.

“Achillean”, so far as I can tell, is a quasi-neologism coined to provide an equivalent term for men/mascs—e.g., gay men and bisexual men attracted to other men would qualify as achillean. “Achillean love” would be love between men/mascs, etc.And that, of course, derives from Achilles, the figure from The Iliad and other myths who famously loved his comrade-in-arms, Patroclus. (Alexander the Great famously considered his lover, Hephaestion, to be pretty much “the Patroclus to his Achilles”).Hope this helps!—Mod Pepper